Chapter 2
Theory
In this chapter a brief description of the electronic structure method is presented.
An introduction to the Density Functional Theory (DFT) and the
approximations used for the calculations of the energies and the bandgaps is
discussed. A condensed overview of the practicalities of the electronic structure
calculations is also presented.
2.1 Schrödinger Equation
A complete quantum mechanical description of a system requires the knowledge
of an abstract object called the wavefunction. In principle, the wavefunction
can be obtained by solving the time dependent Schrödinger equation
which can be written as 5:
i~
@| i
@t
= H| i, (2.1)
where | i and H are the wavefunction and the Hamiltonian of the system
respectively. The Hamiltonian holds the information of the total energy of
the system that is conserved for a time independent potential. Hence, the
stationary state solution to the Schrödinger equation will be a product of the
time dependent phase and a time independent part which is nothing but the
eigenfunction of the Hamiltonian. Therefore, calculating the stationary state
of the Hamiltonian is central to the time independent description of a system.
Since our interest lies in understanding the physical and chemical properties
of materials which are governed by the electrons in time independent potential
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